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TIME-VARYING COINTEGRATION

Published online by Cambridge University Press:  05 March 2010

Herman J. Bierens  and
Luis F. Martins
Herman J. Bierens*
Affiliation:
Pennsylvania State University
Luis F. Martins
Affiliation:
ISCTE Business School
*
*Address correspondence to Herman Bierens, Department of Economics and CAPCP, Pennsylvania State University, 608 Kern Graduate Building, University Park, PA 16802, USA; e-mail: [email protected].
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Abstract

In this paper we propose a time-varying vector error correction model in which the cointegrating relationship varies smoothly over time. The Johansen setup is a special case of our model. A likelihood ratio test for time-invariant cointegration is defined and its asymptotic chi-square distribution is derived. We apply our test to the purchasing power parity hypothesis of international prices and nominal exchange rates, and we find evidence of time-varying cointegration.

Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 5 , October 2010 , pp. 1453 - 1490
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Andersson, S.A., Brons, H.K., & Jensen, S.T. (1983) Distribution of eigenvalues in multivariate statistical analysis. Annals of Statistics 11, 392–415.CrossRefGoogle Scholar
Andrade, P., Bruneau, C., & Gregoir, S. (2005) Testing for the cointegration rank when some cointegrating directions are changing. Journal of Econometrics 124, 269–310.CrossRefGoogle Scholar
Andrews, D.W.K., Lee, I., & Ploberger, W. (1996) Optimal changepoint tests for normal linear regression. Journal of Econometrics 70, 9–38.CrossRefGoogle Scholar
Bai, J., Lumsdaine, R.L., & Stock, J.H. (1998) Testing for and dating breaks in multivariate time series. Review of Economic Studies 65, 395–432.CrossRefGoogle Scholar
Beveridge, S. & Nelson, C.R. (1981) A new approach to the decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle. Journal of Monetary Economics 7, 151–174.CrossRefGoogle Scholar
Bierens, H.J. (1994) Topics in Advanced Econometrics: Estimation, Testing and Specification of Cross-Section and Time Series Models. Cambridge University Press.CrossRefGoogle Scholar
Bierens, H.J. (1997) Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate. Journal of Econometrics 81, 29–64.CrossRefGoogle Scholar
Bierens, H.J. & Martins, L. (2009) Appendix: Time Varying Cointegration. http://econ.la.psu.edu/~hbierens/TVCOINT_APPENDIX.PDF.Google Scholar
Blake, N.S. & Fomby, T.B. (1997) Threshold cointegration. International Economic Review 38, 627–645.CrossRefGoogle Scholar
Caner, M. (1998) Tests for cointegration with infinite variance errors. Journal of Econometrics 86, 155–175.CrossRefGoogle Scholar
De Jong, R.M. (2001) Nonlinear estimation using estimated cointegrating relations. Journal of Econometrics 101, 109–122.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W.J. (1987) Cointegration and error correction:Representations, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Falk, B. & Wang, C. (2003) Testing long run PPP with infinite variance returns. Journal of Applied Econometrics 18, 471–484.CrossRefGoogle Scholar
Granger, C.W.J. (1987) Developments in the study of cointegrated economic variables. Oxford Bulletin of Economics and Statistics 48, 213–218.CrossRefGoogle Scholar
Granger, C.W.J. & Yoon, G. (2002) Hidden Cointegration. Working paper, UCSD.CrossRefGoogle Scholar
Hall, S.G., Psaradakis, Z., & Sola, M. (1997) Cointegration and changes in regime: The Japanese consumption function. Journal of Applied Econometrics 12, 151–168.3.0.CO;2-J>CrossRefGoogle Scholar
Hamming, R.W. (1973) Numerical Methods for Scientists and Engineers. Dover.Google Scholar
Hannan, E.J. & Quinn, B.G. (1979) The determination of the order of an autoregression. Journal of the Royal Statistical Society B 41, 190–195.Google Scholar
Hansen, B.E. (1992) Tests for parameter instability in regressions with I(1) processes. Journal of Business and Economic Statistics 10, 321–335.Google Scholar
Hansen, H. & Johansen, S. (1999) Some tests for parameter constancy in cointegrated VAR-models. Econometrics Journal 2, 306–333.CrossRefGoogle Scholar
Hansen, P.R. (2003) Structural changes in the cointegrated vector autoregressive model. Journal of Econometrics 114, 261–295.CrossRefGoogle Scholar
Hao, K. (1996) Testing for structural change in cointegrated regression models: Some comparisons and generalizations. Econometric Reviews 15, 401–429.CrossRefGoogle Scholar
Harris, D., McCabe, B., & Leybourne, S. (2002) Stochastic cointegration: Estimation and inference. Journal of Econometrics 111, 363–384.CrossRefGoogle Scholar
Inoue, A. (1999) Tests of cointegration rank with a trend break. Journal of Econometrics 90, 215–237.CrossRefGoogle Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.CrossRefGoogle Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.CrossRefGoogle Scholar
Johansen, S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.CrossRefGoogle Scholar
Johansen, S., Mosconi, R., & Nielsen, B. (2000) Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal 3, 216–249.CrossRefGoogle Scholar
Juhl, T. & Xiao, Z. (2005) Testing for cointegration using partially linear models. Journal of Econometrics 124, 363–394.CrossRefGoogle Scholar
Kuo, B.S. (1998) Test for partial parameter instability in regressions with I(1) processes. Journal of Econometrics 86, 337–368.CrossRefGoogle Scholar
Lütkepohl, H., Saikkonen, P., & Trenkler, C. (2003) Comparison of tests for the cointegrating rank of a VAR process with a structural shift. Journal of Econometrics 113, 201–229.CrossRefGoogle Scholar
Lütkepohl, H., Terasvirta, T., & Wolters, J. (1999) Investigating stability and linearity of a German M1 money demand function. Journal of Applied Econometrics 14, 511–525.3.0.CO;2-C>CrossRefGoogle Scholar
Maddala, G.S. & Kim, I.-M. (1998) Unit Roots, Cointegration and Structural Change. Cambridge University Press.Google Scholar
Michael, P., Nobay, A.R., & Peel, D.A. (1997) Transactions costs and nonlinear adjustment in real exchange rates: An empirical investigation. Journal of Political Economy 105, 862–879.CrossRefGoogle Scholar
Park, J.Y. & Hahn, S.B. (1999) Cointegrating regressions with time varying coefficients. Econometric Theory 15, 664–703.CrossRefGoogle Scholar
Phillips, P.C.B. (1988) Weak convergence to the matrix stochastic integral . Journal of Multivariate Time Series Analysis 24, 252–264.CrossRefGoogle Scholar
Phillips, P.C.B. & Durlauf, S.N. (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 473–496.CrossRefGoogle Scholar
Quintos, C.E. (1997) Stability tests in error correction models. Journal of Econometrics 82, 289–315.CrossRefGoogle Scholar
Quintos, C.E. & Phillips, P.C.B. (1993) Parameter constancy in cointegrating regressions. Empirical Economics 18, 675–706.CrossRefGoogle Scholar
Saikkonen, P. & Choi, I. (2004) Cointegrating smooth transition regressions. Econometric Theory 20, 301–340.CrossRefGoogle Scholar
Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics 6, 461–464.CrossRefGoogle Scholar
Seo, B. (1998) Tests for structural change in cointegrated systems. Econometric Theory 14, 222–259.CrossRefGoogle Scholar
Terasvirta, T. & Eliasson, A.C. (2001) Non-Linear error correction and the UK demand for broad money, 1878–1993. Journal of Applied Econometrics 16, 277–288.CrossRefGoogle Scholar